Joseph Hundley, Qiao Zhang
Published 2014-09-30Version 1
In this paper we study the Fourier coefficients of theta functions attached to Dirichlet characters at cusps other than infinity. The method is based on expressing them in terms of explicit elements of the adelic Schwartz space and studying the action of the adelic metaplectic group on these elements. We derive explicit formulae for the Fourier coefficients at all cusps. For the sake of simplicity, some restrictions are placed on the Dirichlet characters considered.
On multiplicativity of Fourier coefficients at cusps other than infinity
Zagier duality and integrality for Fourier coefficients for weakly holomorphic modular forms
A note on Fourier coefficients of Poincaré series
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